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Bart Truyen, Artur Polinski, Jan Cornelis
 

Proceedings SPIE's 8th Annual International Symposium on NDE for Health Monitoring and Diagnostics

Contribution To Book Anthology

Abstract 

Electrical Impedance Tomography (EIT) is concerned with the reconstruction of the electrical properties in the interior of a volume conductor from the application and measurement of voltages and currents on its boundary. Having found different applications in geophysical imaging, more recently EIT also has been identified as a valid candidate technology for the detection and localization of anti-personnel mines. Given its notorious ill-posedness and nonlinearity, straightforward application of EIT, however, is far from obvious for noisy and incomplete data. The disappointing performance of conventional output least squares methods, which seek to minimize the difference between the measured and predicted boundary data from a temptative model, has prompted research into various kinds of regularization, often relying on highly artificial restrictions on the solution. Based on an alternative criterion function, two new problem formulations are derived in this study. Both of them are demonstrated to be equivalent, although exhibiting slightly different numerical properties. Unlike for the output least squares method, the inherent structure of these problem formulations naturally suggest a robust subspace concept. What emerges is an iterative reconstruction method, in which valid solutions are continuously bounded away from spurious noise contributions, to achieve extraordinary stability properties. Furthermore, it is shown how these problem formulations may be further extended also to take into account the noise structure of the stimulation patterns. The performance of this new subspace concept is compared with the recently described variational constraint formulation [G.A. Gray, "A variational study of the electrical impedance tomography problem," SIAM 50th Annual Conference, Philadelphia, PA], this being one of the more promising alternatives. When tested on a set of synthetic problems, the subspace based method clearly demonstrate superior robustness properties, at a significantly reduced computational cost.

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